Consider the toy problem of reporting the approximate sum of \(D = \lbrace x_1, \dots , x_n\rbrace \)  with each \(x_i \in [-1, 1]\) .
A standard way to compute a DP sum is the Gaussian mechanism [1]}:
\(\mathcal {M}(D)= \sum _{x_i \in D} x_i + Z \hspace{14.22636pt}\text{where } Z\sim \mathcal {N}(0,\sigma ^2)\) 
